# SplittingNode(V, C)¶

This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value, that is the current expression to evaluate. The second one is its condition, that is the hypothesis under which the value has to be evaluated. The last one is its status, that is a boolean flag which is true iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).

=: (%, %) -> Boolean
from BasicType
~=: (%, %) -> Boolean
from BasicType
coerce: % -> OutputForm
from CoercibleTo OutputForm
condition: % -> C
condition(n) returns the condition of the node n.
construct: (V, C) -> %
construct(v, t) returns the same as construct(v, t, false)
construct: (V, C, Boolean) -> %
construct(v, t, b) returns the non-empty node with value v, condition t and flag b
construct: (V, List C) -> List %
construct(v, lt) returns the same as [construct(v, t) for t in lt]
construct: List Record(val: V, tower: C) -> List %
construct(lvt) returns the same as [construct(vt.val, vt.tower) for vt in lvt]
construct: Record(val: V, tower: C) -> %
construct(vt) returns the same as construct(vt.val, vt.tower)
copy: % -> %
copy(n) returns a copy of n.
empty: () -> %
empty() returns the same as [empty()\$V, empty()\$C, false]\$\% empty?: % -> Boolean empty?(n) returns true iff the node n is empty()\$\%.
hash: % -> SingleInteger
from SetCategory
hashUpdate!: (HashState, %) -> HashState
from SetCategory
infLex?: (%, %, (V, V) -> Boolean, (C, C) -> Boolean) -> Boolean
infLex?(n1, n2, o1, o2) returns true iff o1(value(n1), value(n2)) or value(n1) = value(n2) and o2(condition(n1), condition(n2)).
latex: % -> String
from SetCategory
setCondition!: (%, C) -> %
setCondition!(n, t) returns n whose condition has been replaced by t if it is not empty, else an error is produced.
setEmpty!: % -> %
setEmpty!(n) replaces n by empty()\\$\%.
setStatus!: (%, Boolean) -> %
setStatus!(n, b) returns n whose status has been replaced by b if it is not empty, else an error is produced.
setValue!: (%, V) -> %
setValue!(n, v) returns n whose value has been replaced by v if it is not empty, else an error is produced.
status: % -> Boolean
status(n) returns the status of the node n.
subNode?: (%, %, (C, C) -> Boolean) -> Boolean
subNode?(n1, n2, o2) returns true iff value(n1) = value(n2) and o2(condition(n1), condition(n2))
value: % -> V
value(n) returns the value of the node n.

BasicType

SetCategory